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Interpretation of Lamellar Electron Diffraction Data from Phospholipids Douglas L. Dorset and Andrew K. Massalski Electron Diffraction Department, Medical Foundation of Buffalo, Inc., 73 High Street, Buffalo, New York 14203

John R. Fryer Chemistry Department, University of Glasgow, Glasgow G 12 8 Q Q Scotland

Z. Naturforsch. 42 a, 381-391 (1987); received October 8, 1986

Lamellar electron diffraction intensity data from a series of optically active 1,2-diradyl phosphatidylethanolamines were used to determine the probable crystal packing, based on translational fitting of the molecular conformation found in the x-ray crystal structure of a dilauroyl homolog. All crystal structures are shown to be similar to one another. A packing model similar to that found from the analysis of lamellar x-ray data from the dimyristoyl homolog is obtained when the measured electron diffraction data are corrected for the curvilinear lamellar deformations seen in direct low dose lattice images.

Crystal Structure Analysis, Crystal Distortion

Introduction

Two decades ago, considerable effort was devoted to the structure analysis of multilamellar biomem-branes, such as myelin, using one-dimensional x-ray diffraction data from well oriented samples [1, 2], a process which often involved interesting techniques for determining crystallographic phases [1-5] . Con-comitant work was also carried out on oriented multilayers of pure phospholipids, and also those incorporating cholesterol [6, 7], The most unequiv-ocal structure analysis of such systems was based on neutron diffraction data which followed the position of deuterium labels in the acyl chains and polar group [8-10], giving conformational results con-sistent with single crystal structure analyses on a small number of diacyl phospholipids [11-15].

After the First crystal structure was reported for a diacyl phosphatidylethanolamine [11], the resultant structural model was used to analyze lamellar x-ray data from a homolog [16], basing this determination on rigid body refinement of a presumed invariant structural conformation for which only overall thermal parameters and molecular shift were permitted to change. Using epitaxial crystallization

Reprint requests to Dr. D. L. Dorset, Electron Diffraction Department, Medical Foundation of Buffalo, Inc., 73 Hight St.. Buffalo, New York 14203, USA.

techniques originally designed for the orientation of polymethylene chain polymers [17], thin lath-like microcrystals of various phospholipids were also grown [18] which give lamellar electron diffraction intensities similar in resolution to the best powder x-ray data from oriented bulk specimens. Although analyses of electron diffraction data based on the known phosphatidylethanolamine crystal structure result in crystallographic residuals similar to the earlier powder x-ray study [16], the refined struc-tures were found to have different packing arrange-ments.

While it is true that phosphatidylethanolamines can crystallize as polymorphic forms [19, 20], avail-able electron diffraction data such as the lamellar spacings [18, 21] indicate that the epitaxially crystallized material should be similar to the struc-tural forms investigated by x-ray diffraction methods. This expectation is supported by the determination of methylene subcell packing with electron diffraction data from solution crystallized samples which also indicate that the molecular chains are untilted [20, 22], A survey of the known phospholipid crystal structures indicates some con-formational freedom in the headgroup region [23] but, by contrast, the conformation of the diacyl glycerol moiety is shown to be extremely con-servative [23], with the same features shown for a variety of phospholipids [11-14], encompassing

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382 D. L. Dorset et al. • Interpretation of Lamellar Electron Diffraction Data from Phospholipids

optically active as well as racemic materials in addition to the numerous headgroup species and conformations. Specifically, the molecular packing and conformation of optically active phosphatidyl-ethanolamines is shown by neutron diffraction analysis [10] to be very similar to the racemic com-pound [11, 12] even when an acetic acid solvent molecule is missing from the headgroup region. For this material this similarity includes the headgroup conformation as well as the axial displacement of acyl chains in the diglyceride portion.

Because the use of electron diffraction data for quantitative structure analyses is still in an early stage of development, it is important to find reasons for discrepancy noted in the earlier determination [19]. From a practical standpoint, since numerous data from direct lattice images and electron diffrac-tion have been obtained from many epitaxially oriented phospholipid samples [24] not yet crys-tallized for single crystal x-ray studies, as well as their solid solutions (D. L. Dorset and A. Massalski, unpublished data), is also will be useful to compare future analyses to the results obtained from a system which is already well defined, such as the phos-phatidylethanolamines.

Materials and Methods

Crystallization of Phospholipids

A homologous series of chiral 1,2-diacyl phos-phatidylethanolamines (dilauroyl, dimyristoyl, di-palmityol) as well as one chiral 1,2-dialkyl phos-phatidylethanolamine (dihexadecyl) were purchased from Calbiochem-Behring (San Diego, Ca.) and were used without further purification. Epitaxial crystallization on a naphthalene substrate was carried out according to the procedure of Wittmann et al. [17] as follows: A small amount of the lipid is dissolved in chloroform and a drop of this solution is allowed to evaporate to dryness on a freshly cleaved mica sheet. Carbon covered electron micro-scope grids are placed over this lipid-containing area and naphthalene crystals are then sprinkled over the surface. The other half of the mica sheet is placed over this physical mixture to form a sandwich and this is moved along a thermal gradient until the naphthalene melts and flows into the space between the sheets, meanwhile solvating the phospholipid layer. The specimen is then cooled so that the

naphthalene crystallization at the eutectic can direct the epitaxial crystallization of the lipid. This places the longest crystallographic axis parallel to the best developed crystal face in contrast to crys-tallization from solution. The sheets are mechanical-ly separated and the naphthalene removed by sub-limation in vacuo to leave the epitaxial phos-pholipid crystals on the grid surface.

Electron Diffraction Data Collection and Microscopy

Selected area electron diffraction patterns at 100 kV were recorded on x-ray film (Kodak DEF-5) using a JEOL JEM-100B electron microscope operated at low incident beam current density to minimize radiation exposure of the sample. Intensity data were obtained from the photographic films by integration under scans made on a Joyce Loebl MklllC flat bed microdensitometer.

Low dose electron micrographs of the thin crys-tals were obtained according to a method given by Fryer [25]. At nearly the same incident beam current as for electron diffraction, images at various values of objective lens defocus were recorded on the same x-ray film at an operating magnification of 20,000x. After a focal series was photographed, the integrity of the specimen was ascertained by observation of the electron diffraction patterns.

Calculations

Kinematical structure factors were calculated in the usual way, i.e.

^oo/= X. /7 e x P 2ft /(/}• • si), /

where f{ is the Doyle-Turner [26] scattering factor corrected for isotropic thermal motion, i.e.

77 = f j • exp ( - B sin2 6/a2) , rj is the atom position in the unit cell and sj is the reciprocal lattice vector. Translational shifts along c are calculated with a suitable computer program based on the function [27], F00i= 2(aA - bB), where a — cos 2 n I za, b = sin 2 n I za,

A = Yj f j c o s 2 n I Zj and B = f j sin 2 n I Zj, j j

for which za is the fractional coordinate of an arbitrary origin and z/ are atomic coordinates with respect to this origin.

383 D. L. Dorset et al. • Interpretation of Lamellar Electron Diffraction Data from Phospholipids

O n e - d i m e n s i o n a l Pa t te rson func t i ons were a lso c a l c u l a t e d in the usual way, i.e.

P(w) = Z ^00/ 2 cos 2n Iz, i

a n d e lec t ros ta t ic potent ia l m a p s (e lec t ron d i f f r a c t i o n a n a l o g to an e lect ron densi ty m a p ) were c o m p u t e d in an a n a l o g o u s f a sh ion to the x-ray case, i.e.

/ <?(--)= F0 + 2 Z ^ 0 0 / c ° s 2n / z ,

1

w h e r e F0 is the m e a n inner po ten t ia l of t he s t ruc-t u r e a n d the FQQ/ a re su i tab ly scaled, p h a s e d s t ruc-t u r e fac tors . It will be no ted tha t c e n t r o s y m m e t r y is a s s u m e d fo r this rec iproca l la t t ice row based on p r e v i o u s s t ruc tura l analysis on p h o s p h o l i p i d s a n d b i o m e m b r a n e s [ 1 - 5 ] . (This is the c o n s e q u e n c e of a 2 j - s c r e w axis p e r p e n d i c u l a r to t he longest uni t cell ax is as f o u n d in the k n o w n p h o s p h o l i p i d crystal s t ruc tu re s [11 - 15].)

N - b e a m d y n a m i c a l cor rec t ions were m a d e in e i t h e r of two ways. In ear ly h a n d ca lcu la t ions , a p h a s e g ra t i ng a p p r o x i m a t i o n [28] was used, i.e. <pool = jrq(z) = ö-iaAtF{00l)

+ F(00l) * F{001) + ...,

w h e r e t he o p e r a t i o n " * " d e n o t e s convo lu t ion . La te r a full mul t i s l ice ca l cu l a t i on [28] was ca r r i ed ou t us ing a c o m p u t i n g p a c k a g e f r o m the Ar i zona S ta te Univers i ty faci l i ty fo r h igh r e so lu t ion e lec t ron mic roscopy . In t he la t t e r ca l cu la t ion t he s t ruc tura l m o d e l was t i l ted 16° a r o u n d [001] to a l low only 0 0 / re f l ec t ions to c o n t r i b u t e to the s t r uc tu r e f ac to r convo lu t ions . Because on ly low ang le d a t a a re used (hence a m i n o r d e v i a t i o n of t he Ewald s p h e r e f r o m the re f lec t ion cen te r ) t h e d i f f e r e n c e b e t w e e n the t w o ca lcu la t ions is very smal l .

Results

Overview A rep re sen t a t i ve e lec t ron d i f f r a c t i o n p a t t e r n f r o m

an ep i tax ia l ly c rys ta l l ized p h o s p h a t i d y l e t h a n o l -a m i n e is s h o w n in F i g u r e 1. L a m e l l a r spac ings of t he p h o s p h o l i p i d s used in th is s tudy a r e g iven in T a b l e 1 in c o m p a r i s o n w i th l i t e r a tu re values . Deta i ls of t h e crystal t e x t u r e a r e r evea led in h igh reso lu t ion e lec t ron m i c r o g r a p h s s h o w n in F i g u r e 2. As dis-cussed e l sewhere [24], t he u n d u l a t i o n of t he lamel lae e x p a i n s the a rc ing of t he 0 0 / d i f f r a c t i o n da t a .

Fig. 1. Electron diffraction pattern of 1,2-dihexadecyl-^«-glycerophosphoethanol-amine (DHPE) epitaxially crystallized on naphthalene. Note arcing of lamellar re-flections.

384 D. L. Dorset et al. • Interpretation of Lamellar Electron Diffraction Data from Phospholipids

Fig. 2. Low dose lattice image of l,2-dipalmitoyl-5AJ-glycerophosphoethanolamine epitaxially crystallized on naphthalene: Note the curvature of lamellae which accounts for the arcing of the electron diffraction patterns as in Figure 1 (see also [24]). Similar images have been obtained from other epitaxially-crystallized phosphatidyl-ethanolamines examined in this study.

Table 1. Lamellar spacing of chiral diradyl phosphatidyl-ethanolamines used for quantitative electron diffraction structure analysis.

Compound t/00I

This study Literature

1,2-Dilauroyl-5«-glycero- 47.7 ± 0 . 5 A 45.2 A (rac) [42] phosphoethanolamine 47.8 A (rac) [ 16] (DLPE) diffraction resolution: / = 14

1.2-Dimyristoyl-™- 49.2 ± 0.4 A 50.0 A (rac) [20] glycerophosphoethanol- 49.9 A (rac) [42] amine (DMPE) diffraction 49.5 A (rac) [16] resolution: / = 15

1,2-Dipalmitoyl-j/i- 55.7 ± 0.5 A 55.0 A (sn) [ 18] glycerophosphoethanol- 55.2 A (rac) [20] amine (DPPE) diffraction 55.3 A (rac) [42] resolution: / = 16 1,2-Dihexadecyl-j«- 5 5 . 2 ± 0 . 5 Ä 55.6 ± 0.5 A glycerophosphoethanol- (sn) [ 19] amine (DHPE) diffraction resolution: / = 16

E l d e r e t al. H i t c h c o c k e t a l .

Fig. 3. Crystal structure of 1,2-dilauroyl-rac-glycero-phosphoethanolamine as determined initially by Hitchcock et al. [11] and then refined by Elder et al. [12]. The view represents the asymmetric unit in the (001) projection of their crystal structure where the abscissa and ordinate are respectively parallel to their a and b axes. (In our study, we have relabeled their longest unit cell a axis as "c" to conform to usual convention in the crystallography of lipids.) Note that there are slight differences in atom positions. These structures were used as models for rigid body refinement after appropriate extension of the poly-methylene chains (see text). A one-dimensional plot of electron density is shown above for this structure. (In this plot, the position of the acetic acid solvent molecule is shown near the origin although it is not represented in the molecular drawing.)

Because of t he s o m e w h a t coa r se s a m p l i n g in te rva l used fo r t r ans l a t ion of the m o d e l s t ruc tu re t h e r e a r e a m b i g u i t i e s in t he r epo r t ed o n e - d i m e n s i o n a l x - ray s t ruc tu ra l analys is of 1 ,2-dimyris toyl rac-phospho-e t h a n o l a m i n e based on the crystal s t ruc tu re of its d i l au roy l h o m o l o g . Th i s d e t e r m i n a t i o n was r e p e a t -ed s ta r t ing wi th sl ightly d i f f e r e n t s t ruc tura l m o d e l s g iven in ear l ies t [11] and la ter [12] r epor t s of t h e d i l au roy l s t ruc tu re (Fig. 3) a n d us ing the r e p o r t e d x- ray d a t a [16]. T o cons t ruc t t he d imyr i s toy l m o d e l , t h e cha ins we re ex t ended a long the i r axes by t he a v e r a g e t r ans la t ion va lue pe r m e t h y l e n e r e p e a t (1.27 A) a n d the pos i t ion of the o u t e r m o s t m e t h y l was p laced at r = 0.5000 in the a p p r o p r i a t e un i t cell. T h e t e m p e r a t u r e fac tors w e r e ass igned acco rd ing to t h e s c h e m e given by Hi t chcock et al. [16], hence

B(z) = ( C + 4.0 + 108 ( r ) 2 ) A 2 (1)

385 D. L. Dorset et al. • Interpretation of Lamellar Electron Diffraction Data from Phospholipids

0 . 5

0.1

0

R O.SH

0.5

10

Structure model Elder et al.

(b)

Structure model Hitchcock et al-

-0.10 -0 .06 -0.02 0 0.02 0.06 0.10 Shift Az

Fig. 4. Rigid body structural analysis with published lamellar x-ray data from 1,2-dimyristoyl-rac-glycero-phosphoethanolamine using models based on the two structures given in Figure 3. The occurrence of minima at slightly different shift positions merely indicate that the polar group positions of the respective models were at different relative locations because the initial z fractional coordinate of the outer methyl carbon is initially at z = 0.5. The sampled shift values in the translation search are at finer intervals than in the original analysis [16], revealing the presence of several minima rather than the single broad one depicted earlier.

for all atoms except for phosphorus where

B(z) = (C + 3.0) A2 . (2)

As in their study, C = 25 A 2 . Results of rigid body search along z are shown in Fig. 4 for the two starting models. The results are basically the same, giving a minimum for the phosphorus position at 0.0515 (49.5 A ) = 2.55 A for the model of Elder et al. [12] and at 0.0497 (49.5 A ) = 2.46 A for the model of Hitchcock et al. [11]. It is apparent therefore that the headgroup position is the most important factor for this structure determination. Due to the presence of an acetic acid solvent

a) DLPE (e.d.) D= 0-14

Fig. 5. One-dimensional Patterson syntheses for experi-mental electron and x-ray diffraction data considered in this work, demonstrating the basic identity of these data which indicate a large peak near 4.0 A and a second between 7 and 8 A. When the electron diffraction data are corrected for crystal texture (see text) the Patterson maps are still similar in appearance, although peaks correspond-ing to longer vectors are more discernable.

molecule, the polar group packing of the multilayer cannot be directly compared to the homolog crystal structure but it is consistent with the phosphorus z-coordinate for a lysophosphatidylethanolamine [29] (z ' c — 2.24 A ) . Observed and calculated struc-ture factors are listed in Table 3.

Patterson Synthesis Patterson functions are shown in Fig. 5 for the

data sets considered in this study. The electron diffraction intensities were taken as they were obtained from integration of densitometer traces without further corrections and placed on a common scale. These are also compared to a Patterson synthesis on lamellar x-ray data from the study of DMPE by Hitchcock et al. [16]. An analysis of the

20

d) DPPE (e.d.) D= 0.11

e) D H P E (e.d.) D=0.12

c) D M P E ( x d ) D=0.12

386 D. L. Dorset et al. • Interpretation of Lamellar Electron Diffraction Data from Phospholipids

Table 2. Results of rigid body refinements on 1,2-dihexa-decyl-s«-phosphoethanolamine based on electron diffrac-tion intensities.

Model Phosphorus position

Start Finish Ä-value

1. Perfect crystal low 0.0379a

temperature factors (C = 0.0A 2) 0.0505b

2. Perfect crystal high temperature factors

a) whole molecule (C = 25 A2)

b) alkyl chains (Bc = 79 A2)

3. Distorted crystal low temperature factors

a) "mosaic" correction for curvilinear lamellae

b) Gaussian correction / > 8

c) Gaussian correction similar to mosaic model

0.0079 -0.0321 0.0055

-0.0345

0.26 0.24 0.26 0.28

0.0505

0.0505

0.0405 * 0.35 0.0005 0.33 0.0055 0.27

0.0505 0.0405 * 0.30 0.0379 0.0379* 0.35

0.0379 0.0079 0.28

0.0379 0.0379* 0.34

This starting position corresponds to the most highly refined crystal structure of DLPE by Elder et al. [12]. This starting position corresponds to the first structure reported for DLPE by Hitchcock et al. [11]. Correct structure.

Table 3. Calculated and observed structure factor values for 1.2-diradyl glycerophosphoethanolamines.

rac DMPE (x-ray) sn DHPE (e.d.)

/ l^ol •^calc / l^ol •^calc

1 13.49 12.99 1 1.20 2.22 2 2.04 0.54 2 0.61 - 0 . 2 6 3 2.50 0.26 3 1.24 1.20 4 5.26 - 6 . 2 0 4 0.70 - 0 . 8 2 5 1.05 - 2 . 0 7 5 0.91 0.09 6 1.95 -2 .07 6 0.54 - 0 . 8 4 7 1.70 - 1 . 2 3 7 0.72 - 0 . 3 4 8 1.75 - 2 . 7 3 8 0.20 - 0 . 4 3 9 4.29 - 4 . 1 6 9 0.62 - 0 . 7 8

10 3.76 - 3 . 4 8 10 0.96 - 0 . 4 3 11 5.53 - 5 . 5 8 11 1.04 - 1 . 2 4 12 4.43 - 3 . 9 6 12 1.65 - 1 . 4 4 13 6.00 - 6 . 3 7 13 1.61 - 1 . 8 6 14 3.73 - 5 . 0 9 14 1.60 - 1 . 7 2 15 2.46 - 3 . 2 0 15 1.47 - 1 . 5 4

16 1.19 - 1 . 0 4 /? = 0.19 R = 0.30

DMPE Patterson map was reported by Khare and Worthington [30]. Three peaks at 4, 7.2 and 11.2 A (see Fig. 5) were interpreted on the basis of inter-molecular vectors, respectively between the phos-phoethanolamine groups (4 A ) and the polar portion of the diglyceride (11.2 A ) , as well as an inter-molecular cross vector between these regions (7.2Ä). This was used to justify a molecular conformation with the polar headgroup bent parallel to the bilayer surface as indicated in other studies [10].

Although some difference exists between the relative scattering factor values in electron diffrac-tion when compared to x-ray diffraction, the computed Patterson functions for the electron diffraction data sets are again quite similar to the one given for the x-ray data set (Fig. 5). i.e. the major peak is at 4 A with a second peak between 7 and 8 A . The exact position of the third peak is less clear. The detectibility of phosphorus, defined

D = Z J p / ^ L ./ l ight atom 1

is approximately the same in electron and x-ray diffraction for the total phospholipid molecule as indicated in Figure 5. However the relative values of the nitrogen and oxygen scattering factors are less than that of carbon in electron diffraction while they are greater in x-ray diffraction. It is apparent, therefore, that phosphorus scattering will have a major role in the electron diffraction from these specimens, although the combined scattering from aligned lighter atoms can also play a similar role to the x-ray scattering case. Given the features of our experimental Patterson maps and the molecular alignment indicated from electron diffraction experiments on solution crystallized samples [19, 11], we carry out our translational search using the untilted molecular packing found for the racemic dilauroyl homolog [11, 12] also preserving the molecular conformation with the anticipation that a solution will be found with polar groups spaced across the polar boundary near w = 4.0 A. In the ensuing discussion this distance will be assessed by finding the position of the phosphorus atom at the ^-value minimum.

Rigid Body Translational Search of Electron Diffraction Data

Rigid body translational searches were carried out for the various data sets used to create the

387 D. L. Dorset et al. • Interpretation of Lamellar Electron Diffract ion Data from Phospholipids

Patterson maps in Fig. 5 after suitable chain length adjustment for the respective molecules in the appropriate unit cell length as discussed above. (For the ether-linked phospholipid, the carbonyl oxygens are excluded from in the structure factor calcula-tions.) In these analyses, three types of models were considered, as discussed in the following and reviewed in Table 2 for the dihexadecyl compound, in an attempt to discover what factors might cause this solution technique to find a false minimum.

(a) Low Temperature Factors, Perfect Crystal

A rigid body model with temperature factors based on (1) and (2) were used with C = 0 . 0 A 2 to simulate a crystal packing with temperature factors similar to the reported crystal structure of the dilauroyl homolog [11, 12], Observed structure factor values were obtained simply as square roots of the observed intensity. A representative transla-tional search is shown in Fig. 6 for the dihexadecyl compound, which is similar to results given earlier from values obtained with a hand calculator [19], These data, as well as those from the dimyristoyl and dipalmitoyl materials, indicate that structural models at two minima give similarly low residuals. These minima correspond to phosphorus coordi-nates respectively in the ranges 0.30 to 0.44 A and - 1.61 to - 1.92 A , values which are clearly incom-patible with the above analyses of x-ray data and the Patterson syntheses on all data sets. Dynamical calculations are found to lower the value of these residuals but do not change the positions of the minima.

(b) High Temperature Factors, Perfect Crystal

Two alternate models were attempted which imposed higher temperature factors on molecular moieties. Using the value C = 25A2 in (1) and (2) for the dimyristoyl and dihexadecyl phosphatidyl-ethanolamines, rigid body translation gives residual minima respectively in the translation intervals 2.23 to 2.33 A and 0.03 to 0.60 A for the phosphorus atom position. If the temperature factors for the molecular moiety in the polar region are adjusted to the values in (1) and (2) for C = 0 . 0 A 2 but with B = 70 A2 for outer chain atoms, similar minima are found e.g. for the dipalmitoyl material. The /^-factor

minima however are not as low as found previously (Figure 6).

(c) Corrections for Crystal Texture

From the appearance of the electron diffraction pattern in Fig. 1 as well as the lattice images in Fig. 2, the crystals used in this structure analysis are far from being perfect. The curvilinear distortion of the lamellar stacking was shown by Vainshtein [31] be equivalent to a distortion of the second kind, commonly referred to as paracrystallinity. Although paracrystalline, the crystals are not mosaic in the usual sense (i.e. there is no pronounced subdivision of the crystals by defects into crystallites). The correction of experimental data for such a texture should nevertheless be similar to a mosaic correc-tion, particularly if the densitometer scans do not record the total intensity of a reflection [32]. Follow-ing Vainshtein [33], the correction for the observed intensity /QO/ can be written as

^ 0 0 / i o b s = ( ^ 0 0 / ' ^ 0 0 / ) 1 / 2 ( 3 )

or, since d*o/ is proportional to the Miller index /,

^ 0 0 / i o b s ^ ( / o o / ' l ) V 2 ,

as is often used to correct lamellar diffraction data from biomembranes [1-5]. Such corrections of lamellar electron diffraction data for all phospho-lipids results in a single residual minimum after rigid body refinement (Fig. 6), giving a phosphorus position in the range 2.08 to 2.76 A . The l v a l u e minima are lower than the thermal model (b) given above but not quite as low as in the first perfect crystal model.

Another type of correction may be envisioned. If the error in intensity measurement is only due to the arced higher order reflection falling outside the width of the densitometer scan, then for a Gaussian function

/ ( x ) = exp ( - h 2 x 2 / l 2 )

the half width l/h of a reflection along x ± z* is dependent on the Miller index /. If reflections beyond say / = 8 are incompletely measured by the densitometer, the observed intensity can be correct-ed after finding the fraction of the Gaussian area outside the scan width. After numerical integration of such a Gaussian model and a translational search

388 D. L. Dorset et al. • Interpretation of Lamellar Electron Diffraction Data from Phospholipids

- 0 1 0 - 0 . 0 6 -0 .02 0 0.02 0.06 0.10 Shift Az. -0.10 - 0 . 0 6 -0 .02 0 Q02 0 .06 0.10 Shift Az

Fig. 6. Rigid body translational searches using electron diffraction data (a) DHPE, low temperature factors, no correction for lamellar curvature, (b) DHPE, high temperature factors, no correction for lamellar curvature, (c) DHPE low temperature factors, correction for lamellar curvature, (d) DMPE, low temperature factors, no correction for lamellar curvature (e) DMPE, low temperature factors, correction for lamellar curvature, (f) DLPE, low temperature factors, correction for lamellar curvature.

with corrected intensity from dihexadecyl phos-phatditylethanolamine, a minimum is found again corresponding to a phosporus position at z • c = 0.43 Ä. In the more extreme case, i.e. if only a central section of the intensity of each reflection is measured by the densitometer, then the correction is similar to (3) above and the rigid body search with corrected data gives a minimum again at z • c = 2.23 A for phosphorus. A comparison of cal-culated and observed structure factors is shown in Table 3 which represents a correction to observed data according to (3).

Electrostatic Potential M a p s

Electrostatic potential maps are calculated in one dimension using the phases obtained from the R-

value minimum which best conforms to the known crystal structure (see Table 2) and observed struc-ture factors respectively assuming a perfect and a distorted crystal (Figure 7). These are compared to maps made from calculated structure factors based on the three models discussed above. Since the features of a structure map largely depend on the phase assignments [34], it is not surprising that these are all very similar to one another. However, a comparison of corresponding densities for a map obtained from calculated structure factor to maps calculated with observed data respectively assuming a perfect or a distorted crystal (Fig. 8) readily shows that the least overall deviation from the line of perfect correlation occurs when a correction is made for crystal distortion. On a quantitative basis, using a curve fitting routine and assuming a linear relationship between the two data sets, it is found

DHPE Model 2a

DHPE Model

389 D. L. Dorset et al. • Interpretation of Lamellar Electron Diffraction Data from Phospholipids

Fig. 7. Electrostatic potential maps for 1,2-dihexadecyl-5«-glycerophosphoethanolamine (DHPE) using: (a) Fc with phases at shift Az = - 0.01, (b) Fobs with same phases but no correction for lamellar curvature and (c) Fobs with same phases but also with correction for lamellar curvature. The First and largest peak on the left corresponds to the phosphoethanolamine moiety, the second to the glycerol region and the latter region to the long chains (compare to Figure 3).

that a scale factor should be applied in both com-parisons. After this, the respective correlation coefficients [35] for the maps calculated from un-corrected observed structure factors to the one obtained from calculated structure factors are 0.88 and 0.94.

Discuss ion

Refinement space is multivariate and with a number p parameters being refined against n observed data, there can be many local minima in the crystallographic residual which may be nearly the same value. The possibility to distinguish a correct solution among alternative structural models can be particularly difficult when there are a small

data

Fig. 8. Correlation of density in electrostatic potential maps in Fig. 7. (a) Comparison of map density of Fig. 7 a with Figure 7 b; (b) comparison of map density of Fig. 7a with Figure 7 c. The line at 45° indicates a perfect correla-tion with no need for a scaling factor (only approximately true, see text). The second comparison of structures is found to give best agreement.

number of observed data [27]. In the rigid body translational search of the dimyristoyl phosphatidyl-ethanolamine (DMPE) crystal structure using x-ray data discussed above, the conformational integrity of a shorter chain homolog is assumed to be a reasonable model. Nevertheless there are at least three variables in this analysis, i.e. scale factor, translation coordinate and overall temperature

390 D. L. Dorset et al. • Interpretation of Lamellar Electron Diffraction Data from Phospholipids

factor for >7=15 observed data. Following the statistical analysis given by Hamilton [36] (and assuming unit weight for calculation for the residual), the significance of an /^-factor is based on

p. n-p. x n — p F + 1 1 p. n-p. 2 ' 1

1/2

where F is a distribution function and I is the significance level of the test. Thus for two structural models with /^-values R\ and R0 where R0 is the smallest, the model with Rj can be rejected only if R\>-^p.n-p.iRo- In the x-ray study then, p = 3, n — p = 12 and from Table 4 of Hamilton's book [36] ^3,12,0.05 = 3.4903 leading to 12,0.05 = 1-37. Thus, although the lowest R-\alue minimum found for DMPE is 0.16, within these refined parameters any other model up to R = 0.22 cannot be excluded. From the sharpness of minima in Fig. 4, other minima in the residual curve for which only molec-ular translation is changed can be clearly rejected. The structural result also appears to be meaningful and, as mentioned above, is consistent with a one dimensional neutron diffraction structure analysis on a chiral dipalmitoyl homolog [10].

The picture is not so straightforward for the structure determination with electron diffraction data. In our considerations above we can include at least five variable parameters - i.e. scale factor, two temperature factors (for polar region and chains), molecular shift and crystal texture (the latter variable is assumed in the x-ray refinement). For the phospholipid DHPE which give the "best" structural results (i.e. lowest 7?-factor), p = 5 and n = 16. Testing at the 1 = 0.05 confidence level, we find

1 .0 .05 3.2039 + 1 1/2

= 1.57.

Hence, although the lowest R-Value shown in Table 2 is 0.24, we can accept models with residuals up to 0.38 as being equally probable. This includes a model where the data are corrected for lattice distortion and which refines to a position similar to the one found in the x-ray analysis. Compared to earlier structure analyses with x-ray data [30]. the / l va lue for the correct solution is not unreasonable.

The correctness of these assumptions can be supported with other data. To review, comparison

of unit cell "long spacings" from these chiral phosphatidylethanolamines to those from the racemic forms shows that they are very similar and are likely not to be a tilted polymorph (Table 1). Electron diffraction data from solution grown crys-tals. which only allow one to discern the features of the acyl chain packing [37]. also indicate the chain axes to be untilted and to pack in a methylene subcell similar to the one found for the racemic DLPE [19, 22], Chains of the dialkyl lipid DHPE has been shown to pack in the hexagonal methylene subcell [19] which is also untilted. Electron micro-graphs in Fig. 2 clearly indicate that the crystals undergo a plastic deformation of the lamellae which has already been shown for solution grown samples to be a property peculiar to such lipids [38]. This justifies the type of correction used to the observed diffraction data and leads to the identification to a physically resonable packing model similar to the results obtained from x-ray data and single crystal determinations. Recalculation of Patterson maps after the observed data are corrected for crystal texture, still gives a pronounced peak near 4.0 A but also improves the visibility of peaks due to longer vector interactions. Calculations of Patterson maps at various translational positions of the phasing model was shown to provide the best match to the map produced from observed data (i.e. a cross-correlation) when the physically reasonable solution is reached. Such a match of autocorrelation func-tions may therefore be more meaningful than R-factor minima.

It is also important to stress here that electron diffraction structure analyses cannot be carried out in a dogmatic way - i.e. a universal model for crystal texture cannot be applied in all cases [39]. For example, the best description of many solution-grown samples, i.e. a bend deformed perfect crystal, also appears to hold for the best epitaxially-crystal-lized polymethylene crystals such as n-paraffins for quantitative structure analysis [40]. With the recent demonstration of lattice imaging for both solution-[41] and epitaxially- [25] crystallized paraffin crystals, it is nevertheless important to obtain even low resolution (e.g. 16 A ) images of the crystal texture first in order to discern what model is best applied to a particular electron crystal structure analysis. Only then, as demonstrated here, can structural interpretations be made which have physical meaning.

391 D. L. Dorset et al. • Interpretation of Lamellar Electron Diffraction Data from Phospholipids

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